Among a variety of social games played on mobile phones, card battle type games have gained popularity. Each card typically has an associated rarity ranking (e.g., common, uncommon, and rare) and rare cards are difficult for users to obtain. Users can collect cards from sets of thousands of cards in collections associated with the game and distributed from a game server. Rare cards are more valuable because of their limited availability and the value of the contents of the card. However, after the users obtain many rare cards as a result of playing the game for a long period of time, the user typically loses their interest to continue playing the game because the user has experienced all, or substantially all, of the finite number of the available rare cards.